To find the slant height of a square pyramid, we can use the Pythagorean theorem. The slant height can be found by finding the hypotenuse of a right triangle formed by the height of the pyramid and half the length of the base.
Let's assume the height of the pyramid is 7 in and the length of the base is 16 in.
Using the Pythagorean theorem, we have:
a^2 + b^2 = c^2
where a is the height of the pyramid, b is half the length of the base, and c is the slant height.
Substituting the given values, we have:
7^2 + (16/2)^2 = c^2
49 + 8^2 = c^2
49 + 64 = c^2
113 = c^2
Taking the square root of both sides, we find:
c ≈ √113 ≈ 10.63
Therefore, the slant height of the square pyramid is approximately 10.63 inches.